Algebraic Expression
Like terms:Algebraic expressions which has same variables and its power is same.
for eg: 23cd,34cd are like terms.Unlike terms:Algebraic expression which has not same variable and
same variable has not same power is called unlike terms,
for eg:3xy,3ab are unlike terms. |
ADDITION:Only like terms of algebraic expression can be added.Value of variables will remain same,
only constants are added
SUBTRACTION:Only like terms of algebraic expressions can be subtracted.Value of variable will remain same,
only constants are subtracted. |
| Multiplication:Unlike addition and subtraction where only constants value changes.
In multiplication both variales and constants are multiplied. Variables are multiplied using exponents rule.
| DIVISION: In division both variables and constants are divided.Variables are divided using exponents rule.
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ADDITION AND SUBSTRACTION OF ALGEBRAIC EXPRESSION
Ex 1: Add the algebraic expression 3xy+4x^3y-14ab,4xy-30x^y+3ab
ans:(3+4)xy + (4-30)x^2y+(-14+3)ab
=7xy-14x^y -11ab
check the answer!!!
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Ex 2:Subtract the Algebraic expression 3xy+4x^3y-14ab,4xy-30x^y+3ab
ans:(3-4)xy + (4+30)x^2y+(-14-3)ab
=-xy +34x^y -17ab
check the answer!!!
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TRY OUT BY YOURSELF
1.Add the following equation:
a)13x^2yz + 45x^2y,12x^2y - 30x^2yz
b)23abc + 12cd-23bc,23cd-12abc-34bc
c)34lmn-12p + 56qr,-19lmn-12p-90qr
d)980lmn-60p^2-69qr,-980lmn-30p^2-30qr
2.Subtract the following equation:
a)(13x^2yz + 45x^2y)-(12x^2y_30x^2yz)
b)(23abc + 12cd-23bc)-(23cd-12abc-34bc)
c)(34lmn-12p + 56qr)-(-19lmn-12p-90qr)
d)(980lmn-60p^2-69qr)-(980lmn-30p^2-30qr)
1 Ans: a)-17x^2yz+57x^2y
b)11abc +35cd -57bc
c)15lmn-24p -34qr
d)-90p^2-99qr
MULTIPLICATION AND DIVISION OF ALGEBRAIC EXPRESSION
Ex 1:Multiply 6x^2z,12y^2z
Ans:6x^2z,12y^2z
= (6*12)*x^2*y^2*z^(1+1)
= (6*12)*x^2*y^2*z^2
= 72x^2y^2z^2
check the answer!!!
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Ex 2:Divide 45abc^2/3abc
Ans:(45/3)*a(1-1)*b(1-1)*c(2-1)
=15a^0b^0c^1= 15c
check the answer!!!
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TRY OUT BY YOURSELF
1.Simplify the following equation:
a)3x-2(10x+12x^2-3x^2y)
b)3xy*10xy- 5xy/10x
c)(5lmn+20n-3m)*4m
d)(3x-2)*(2y-4)
e)4xy^2z/2xy
f)(3ab-2ac)/2a
g)2xy/3 + 4xy/5 - 3xy/8
h)3z-2(36xy/y - 48xyz/12yz + 45a/10)
Ans:a)3x-20x-24x^2+6x^2y b)30(xy)^2-y/2 c)20lmn^2 -12m^2 d)6xy-12x-4y +8
e)2yz f)(3b/2)-c g) xy(2/3 + 4/5 -3/8) h)3z-64x-9a
WORD PROBLEMS
1.Suresh has Rs3456 in bank.Suresh's sister has also some fixed amount of money in bank.The total
amount of money in banknis Rs.455678.Find the amount of Suresh's sister money in bank.
Let Suresh's sister sge be x.
x+3456=455678
x=455678-3456
45222
check the answer!!!
2. Sohan's son age is 3th of Sohan's age,difference between
their ages is 44.Find their ages.
Ans: let Sohan age would be x,
Sohan's son age is x/3.
x+x/3=44
4x/3=44
x=33,x/3=11
their ages are 33,11
check the answer!!!
3. Mahesh age is 1/2 of Suresh age.After 10 years their age difference will be 4 . Find their present age.
Let Suresh age be x
,Mahesh age would be x/2
After 10 years,(x+10)-{(x/2)+10 }
=x-x/2+10-10=4
=(2x-x)/2=4
2x-x=4
x=8
check the answer!!!
4. Akash age is 1/3 of Suresh age.After five years Akash age would be 1/2 of Suresh age.Find their present age.
5. Rohan bought x number of apples and (1/3)x number of oranges, no of total fruits are 344.Find the no of apples,no of oranges.
6.The cost of eggs are Rs.60 per dozen,Suresh pays Rs.1120 to shopkeeper for eggs.
Find the number of eggs Suresh bought.
7.Sohan has one cardboard having length 4/5 of his breadth.Perimeter of cardboard is 540cm.Find the length
and breadth.
8.Perimeter of a square box is 6400cm.Find the side of the square.
9.Rakesh has some amount of money, he pays 3/5 to Prakash. Find the money Prakash got, when the
left amount is Rs.56000 with Rakesh after giving to Prakash.
10.Mohan's age is 1/2 of his father's age and their age difference is 22.Find their ages.
Ans:4. Akash age= 15years old,suresh age=10years old 5:number of apples= 258, number of oranges= 86
6:5600 eggs 7: breadth=150cm,length=120cm 8.1600cm 9:84000 10:Mohan age=22years old Mohanfather age= 44years old